I am having trouble cutting medium density chipboard (non-corrugated cardboard) with my cutter. First the board would not stick to the mat. I sanded the back of it, then washed the mat with soap and water and resprayed it with Kryon Easy Tack. That solved that problem - mostly. The board stuck to the mat where the rollers moved over it and I had to scrape some of it off. Fortunately the damage to the board did not show and I am glueing the pieces back to back to make the resulting template thicker.
I used a long 60 degree blade on my old Black Cat Pro. I used a Speed of 100 and started with a pressure of 80, which was later changed upwards to 100, 120 and then 200. I started with the blade up and then moved it down by about a half turn twice. The first cut worked, but only after about 15 passes. We turned the mat around and began from the other end (in order to use all of the chipboard and not have trouble with the rollers moving off the back of the board. The first cut worked. Speed at 100, Pressure at 200 and blade dialed upwards. We turned the blade down for the next cut - and disaster struck. The mat slipped and the blade cut away from the original lines. It was stopped in time for me to take the result off the board and cut through the remaining board with scissors (for the straight bits) and with a craft knife (for the fiddly bits). Once again, the damage will not show because I am laminating identical cutouts together.
All this is much less than ideal. I presume that I have the settings wrong. I cannot find any clear instructions on how to set the blade depth (which may be the problem.) The blade is new and therefore at peak sharpness. The cardboard sticks OK to the mat, now, so that is not the problem. So that leaves Pressure, Speed and Blade set up as the probable culprits.